Quasi-Banach Schatten–von Neumann properties in the Weyl–Hörmander calculus

We study structural properties of [Formula: see text], which are Wiener–Lebesgue spaces with respect to a slowly varying metric [Formula: see text] and with parameters [Formula: see text], [Formula: see text]. For [Formula: see text], we deduce Schatten-[Formula: see text] properties for pseudo-differential operators whose symbols, together with their derivatives, obey suitable [Formula: see text]-boundedness conditions. Especially, we perform such investigations for the Weyl–Hörmander calculus. Finally, we apply our results to global-type SG and Shubin pseudo-differential operators.